Scenario generation

It approximates the expectation of the stochastic formulation (usually called the true problem) and can be solved using deterministic algorithms. Problem (9.19) can be solved iteratively in order to provide statistical bounds on the optimality gap of the objective function value. The iterative SAA procedure steps are explained in Section 7.5 of Chapter 7. 

The modeling system GAMS (Brooke et al, 1996) is used for setting up the optimization models. The computational tests were carried out on a Pentium M 

Production capacity Higher limit (103t/year)  

The problem was solved for different sample sizes N and N to illustrate the variation of optimality gap confidence intervals, while fixing the number of replications I to 30. The replication number R need not be very large to get an insight into Vn variability. Table 9.3 shows different confidence interval values of the optimality gap when the sample size of N assumes values of 1000, 2000, and 3000 while varying N from 5000, 10 000, to 20 000 samples. The sample sizes N and N were limited to these values due to increasing computational effort. In our case study, we ran into memory limitations when N and N values exceeded 3000 and 20 000, respectively. The solution of the three refineries network and the PVC complex using the SAA scheme with N = 3000 and N = 20000 required 1114 CPU s to converge to the optimal solution. 

Product Sale price ( /ton) Process technology Process index Min Econ. Prod. (103 t/year) 

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A 5% standard deviation from the mean value of market demand for the saleable products in the LP model is assumed to be reasonable based on statistical analyses of the available historical data. To be consistent, the three scenarios assumed for price uncertainty with their corresponding probabilities are similarly applied to describe uncertainty in the product demands, as shown in Table 6.2, alongside the corresponding penalty costs incurred due to the unit production shortfalls or surpluses for these products. To ensure that the original information structure associated with the decision process sequence is respected, three new constraints to model the scenarios generated are added to the stochastic model. Altogether, this adds up to 3 x 5 = 15 new constraints in place of the five constraints in the deterministic model. 

The remainder of this Chapter 9 is organized as follows. In Section 9.2 we will explain the proposed model formulation for the refinery and petrochemical integration problem under uncertainty. Then, in Section 9.3, we will explain the scenario generation methodology adopted. In Section 9.4, we present the computational... 

The issue of scenario generation can be looked at from a content and a process perspective. The content perspective deals with the question of... 

Mearns L.O. Bogardi I. Giorgi F. Matyasovsky I. and Palecki M. (1999). Comparison of climate change scenarios generated from regional climate model experiments and statistical downscaling. J. Geophys. Res., 104(D6), 6603-6621. 

A solution generated by the (naive) chase is called a canonical solution. It is possible to prove [Fagin et al. 2005a] that each canonical solution is a universal solution. Chasing the s-t tgds in our example scenario generates the canonical, universal... 

Fig. 9.7 Basic scenario expansion and synthetic scenario generation...

Meteoritic impacts delivered natural and unnatural amino acids to Earth, especially in the early phases. The prebiotic soup and/or the FeS scenario produce amino acids as racemates. In contrast to the RNA world, diverse reactions in five different scenarios generated peptides. 

Humans in the system can be treated in the same way as automated components in step 1 of STPA, as was seen in the interlock system above where a person controlled the position of the door. The causal analysis and detailed scenario generation for human controllers, however, is much more complex than that of electromechanical devices and even software, where at least the algorithm is known and can be evaluated. Even if operators are given a procedure to follow, for reasons discussed in... 

The QA process model then is used to generate complete QA process scenarios. The process of failure scenario generation is shown in Fig. 4 and also explained as follows ... 

Firstly the accident evolutions have been studied as combination of Basic Events intended as simple events describing independently the evolution of the scenario generated by the Starting Event. 

Klibi and Martel (2012) D S DP, TR RE SP QN, EX Monte-Carlo for scenario generation risk evaluation in the second stage... 

Chapter 14 gives a detailed example of conducting a probabilistic risk assessment of launching a payload into space. Accident scenario generation, event trees, consequence determination, and uncertainty are described and worked through. It also discusses how this information can be used to determine safety costs. 

Scenario generation—Training system must be capable of generating scenarios for practicing basic training functions. 

Illustrative Scenarios Generation IV Performance Against Goals, Chapter 3 of the Report of the Generation IV Fuel Cycle Crosscut Group, October 1001, at http //www. gif.inel. gov/roadman/... 

Trucco, P, Petrenj, B. De Ambroggi, M. 2014 Ontology-based Disruption Scenario Generation for Critical Infrastructure , Proceedings of PSAM12, June 2014, Honolulu. 

High system pressures are needed to compensate for the low heat capacity of He and to achieve high thermal efficiency for CO2, respectively. Highly pressurized systems require special design provisions to mitigate the potential for and consequences of rapid depressurization scenarios. Generation IV GFRs have provisions for heat removal from the core in accident scenarios and in planned maintenance processes. 

Martin, G.A., Hnghes, C.E. A Scenario Generation Framework for Automating Instructional Support in Scenario-based Training. In Proceedings of the Spring Simulation Multiconference (2010)... 

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